Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, k, m
from proveit.numbers import Exp, Mult, Neg, Sum, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _alpha_m, _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(_alpha_m, Mult(frac(one, _two_pow_t), Sum(index_or_indices = [k], summand = Mult(Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))), Exp(e, Mult(two, pi, i, _phase, k))), domain = _m_domain)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\alpha_{m}, \frac{1}{2^{t}} \cdot \left(\sum_{k = 0}^{2^{t} - 1} \left(\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 52
2	Operation	operator: 45 operands: 5
3	Literal
4	ExprTuple	52
5	ExprTuple	6, 7
6	Operation	operator: 38 operands: 8
7	Operation	operator: 9 operand: 11
8	ExprTuple	44, 43
9	Literal
10	ExprTuple	11
11	Lambda	parameter: 51 body: 13
12	ExprTuple	51
13	Conditional	value: 14 condition: 15
14	Operation	operator: 45 operands: 16
15	Operation	operator: 17 operands: 18
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	51, 21
19	Operation	operator: 47 operands: 22
20	Operation	operator: 47 operands: 23
21	Operation	operator: 24 operands: 25
22	ExprTuple	27, 26
23	ExprTuple	27, 28
24	Literal
25	ExprTuple	29, 30
26	Operation	operator: 40 operand: 35
27	Literal
28	Operation	operator: 45 operands: 32
29	Literal
30	Operation	operator: 33 operands: 34
31	ExprTuple	35
32	ExprTuple	53, 49, 50, 36, 51
33	Literal
34	ExprTuple	43, 37
35	Operation	operator: 38 operands: 39
36	Literal
37	Operation	operator: 40 operand: 44
38	Literal
39	ExprTuple	42, 43
40	Literal
41	ExprTuple	44
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operands: 48
44	Literal
45	Literal
46	ExprTuple	53, 49, 50, 51, 52
47	Literal
48	ExprTuple	53, 54
49	Literal
50	Literal
51	Variable
52	Variable
53	Literal
54	Literal